Convergence of dynamic programming principles for the p-Laplacian
del Teso, F., Manfredi, J. J., & Parviainen, M. (2020). Convergence of dynamic programming principles for the p-Laplacian. Advances in Calculus of Variations, Ahead of print. https://doi.org/10.1515/acv-2019-0043
Published inAdvances in Calculus of Variations
DisciplineMatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)
© 2020 Walter de Gruyter GmbH, Berlin/Boston
We provide a unified strategy to show that solutions of dynamic programming principles associated to the p-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.
Dirichlet problem dynamic programming principle discrete approximations asymptotic mean value properties convergence monotone approximations viscosity solution generalized viscosity solution equivalent notions of solutions numerical methods approksimointi osittaisdifferentiaaliyhtälöt numeeriset menetelmät
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Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF
Additional information about fundingThe first author is supported by the Toppforsk (research excellence) project Waves and Nonlinear Phenomena (WaNP), grant no. 250070 from the Research Council of Norway, and by the grant PGC2018-094522-B-I00 from the MICINN of the Spanish Government. The third author is supported by the Academy of Finland project no. 298641.
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